Equation of the line passing through the point (-6,-3) and perpendicular to the line passing through (-2,7) and (6,5) is y = 4x -19.
First we will find the slope of the line passing through (-2,7) and (6,5).
Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.
We know that,
Product of the slopes of two perpendicular lines = -1.
Let the equation of the line we have to find be y = mx + c.
Slope will be m.
Hence, we can write,
m*(-1/4) = -1
m = -1*(-4/1)
m = 4
Putting (6,5) and m = 4 in y = mx + c , we get
5 = 4*(6) + c
5 = 24 + c
c = 5 - 24 = -19
Hence, the equation of the line is:-
y = 4x -19
To learn more about slope of the line, here:-
https://brainly.com/question/16180119
#SPJ1
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
i inserted a picture of the question, could you please take the short way.
Recall the following property of exponents:
[tex](a\cdot b)^x=a^x\cdot b^x\text{.}[/tex]Therefore:
[tex](14\cdot(-58))^{16}=14^{16}\cdot(-58)^{16}\text{.}[/tex]Answer: Option A.
Type the correct answer in each box use numerals instead of words What are the values of the function
Given the following function:
[tex]h(x)=\begin{cases}{3x-4;x<0} \\ {2x^2-3x+10;0\leq x<4} \\ {2^x};x\ge4\end{cases}[/tex]We will find the value of the function when x = 0 and when x = 4
First, when x = 0, the function will be equal to the second deifinition
So, h(0) will be as follows:
[tex]h(0)=2(0)^2-3(0)+10=10[/tex]Second, when x = 4, the function will be equal to the third definition
So, h(4) will be as follows:
[tex]h(4)=2^4=16[/tex]So, the answer will be:
[tex]\begin{gathered} h(0)=10 \\ h(4)=16 \end{gathered}[/tex]PLEASE HELP! *not a test, just a math practice that I don't understand.
1) Let's analyze those statements according to the Parallelism Postulates/Theorems.
8) If m∠4 = 50º then m∠6 =50º
Angles ∠4 and ∠6 are Alternate Interior angles and Alternate Interior angles are always congruent
So m∠4 ≅ m∠6
9) If m∠4 = 50, then m∠8 =50º
Angles ∠4 and ∠8 are Corresponding angles and Corresponding angles are always congruent
10) If m∠4 = 50º, then m∠5 =130º
Angles ∠4 and ∠5 are Collateral angles and Collateral angles are always supplementary. So
≅
An online company is advertising a mixer on sale for 25 percent off the original price for 260.99. What is the sale price for the mixer . Round your answer to the nearest cent , if necessary.
$195.74
1) We can find out the sale price for the mixer, by writing out an equation:
In the discount factor 1 stands for 100% and 25% =0.25
2) So we can calculate it then this way:
[tex]\begin{gathered} 260.99(1-0.25)= \\ 260.99\text{ (0.75)=}195.74 \\ \end{gathered}[/tex]Note that we have rounded it off to the nearest cent 195.7425 to 195.74 since the last digit "4" is lesser than 5, we round it down.
3) So the price of that mixer, with a discount of 25% (off) is $195.74
Alternatively, we can find that price by setting a proportion:
0.25 = 1/4
Writing out the ratios we have:
260.99 --------- 1
x ---------------- 1/4
Cross multiplying it we have:
260.99 x 1/4 = x
x=65.2475
Subtracting that value 25% (65.2475) from 260.99 we have:
260.99 - 65.2475 =195.7425 ≈ 195.74
Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
The annual fixed expense for car insurance is $ 1,046.70.
It is given in the question that John makes six payments in a year at $174.45 each.
We have to find the annual fixed expense for car insurance.
We know that,
The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.
Hence, by simple multiplication, we can write,
Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70
Car insurance
Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.
To learn more about multiplication, here:-
https://brainly.com/question/5992872
#SPJ1
the x intercept of a functions is called?
In this case, the answer is very simple:
x
An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away. A group of scientists has designed a spaceship that can travel at the speed of 7 x 108 kilometers per year. How many years will the spaceship take to reach the extrasolar planet?
Speed is the time rate at which an object is moving along a path. Then 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
What is Speed?Speed is the time rate at which an object is moving along a path.
The formula for speed is distance/time
Given that
An extrasolar planet is observed at a distance of 4.2 x 10° kilometers away.
Distance= 4.2 x 10°
A group of scientists has designed a spaceship that can travel at the speed of 7 x 10⁸ kilometers per year
Speed = 7 x 10⁸
Time we need to calculate
Time =Distance/speed
Time = 4.2 x 10°/7 x 10⁸
=0.6×10⁻⁸
Hence 0.6×10-8 years will the spaceship take to reach the extrasolar planet.
To learn more on Speed click:
https://brainly.com/question/28224010
#SPJ2
which expression could be substituted for x in the second equation to find the value of y?
Substitution
We have the system of equations:
x + 2y = 20
2x - 3y = -1
To solve it with the substitution method, we need to solve the first equation for x and substitute it in the second equation.
Subtracting 2y to the first equation:
x = -2y + 20
This expression corresponds to choice B.
decide whether the events are independent or dependent and explain your answer.-drawing a ball from a lottery machine, not replacing it, and then drawing a second ball.
If the probability of an event is unaffected by other events, it is called an independent event. If the probability of an event is affected by other events, then it is called a dependent event.
A ball is drawn from a lottery machine. Then, a second ball is drawn without replacing the first ball. Let T be the number of balls in the lottery machine initially. Before the first ball is drawn, the number of balls in the machine is T. At the time the second ball is drawn, the number of balls in the machine is T-1. From T-1 balls, the second ball is drawn. So, the event of drawing the second ball is affected by the event of drawing the first ball.
Therefore, the event of drawing a ball from a lottery machine, not replacing it, and then drawing a second ball is a dependent event.
Type the correct answer in each box.1020PX1150Parallel lines pand gare cut by two non-parallel lines, mand n, as shown in the figure.►gmnThe value of xisdegrees, and the value of y isdegrees.ResetNext
EXPLANATION
Given the parallel lines that are cutted by two non-parallel lines, m and n, the supplementary angle to 102 degrees is by the supplementary angles theorem 180-102= 78 degrees.
By the alternate interior angles theorem, the value of x is 78 degrees.
Also, by the corresponding angles theorem, the value of y is 115 degrees.
A boutique in Lanberry specializes in leather goods for men. Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This month, they sold 94 wallets and 22 belts, for a total of $3,230. How much does the boutique charge for each item?
Let w represent the cost of each wallet.
Let b represent the cost of each belt.
Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that
56w + 63b = 3920
This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that
94w + 22b = 3230
We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be
5264w + 5922b = 368480
5264w + 1232b = 180880
Subtracting the second equation from the first, we have
5264w - 5264w + 5922b - 1232b = 368480 - 180880
4690b = 187600
b = 187600/4690
b = 40
Substituting b = 40 into 56w + 63b = 3920, we have
56w + 63(40) = 3920
56w + 2520 = 3920
56w = 3920 - 2520 = 1400
w = 1400/56
w = 25
Thus, the boutique charges $25 for each wallet and $40 for each belt
What is the value of x if x + 15 = 38 ? Enter answer below
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
This figure shows two similar polygons; DEFG∼TUVS. Find the value of x.
According to the question, both polygons are similar. It means you can use proportions to find the value of x.
[tex]\frac{DE}{TU}=\frac{EF}{UV}[/tex]Replace for the given values in the picture
[tex]\begin{gathered} \frac{x}{6}=\frac{4}{12} \\ x=\frac{4}{12}\cdot6 \\ x=2 \end{gathered}[/tex]x has a value of 2.
Simplify 6+ √-80.
06+16√5i
06+4√5
06+16/ √5
06+4√ √5i
Answer:
6 + 4[tex]\sqrt{5}[/tex]i
Step-by-step explanation:
The prime factorization of 80 is 2x2x2x2x5
6 + [tex]\sqrt{-2x2x2x2x5}[/tex] We can take out 2 pairs of 2 which would be 4 and [tex]\sqrt{-1}[/tex] is i
6 + 4[tex]\sqrt{5}[/tex] i
hi i dont understand this question, can u do it step by step?
Problem #2
Given the diagram of the statement, we have:
From the diagram, we see that we have two triangles:
Triangle 1 or △ADP, with:
• angle ,θ,,
,• hypotenuse ,h = AP,,
,• adjacent cathetus, ac = AD = x cm.
,• opposite cathetus ,oc = DP,.
Triangle 2 or △OZP, with:
• angle θ,
,• hypotenuse, h = OP = 4 cm,,
,• adjacent cathetus, ac = ZP = AP/2,.
(a) △ADP: sides and area
Formula 1) From geometry, we know that for right triangles Pitagoras Theorem states:
[tex]h^2=ac^2+oc^2.[/tex]Where h is the hypotenuse, ac is the adjacent cathetus and oc is the opposite cathetus.
Formula 2) From trigonometry, we have the following trigonometric relation for right triangles:
[tex]\cos \theta=\frac{ac}{h}.[/tex]Where:
• θ is the angle,
,• h is the hypotenuse,
,• ac is the adjacent cathetus.
(1) Replacing the data of Triangle 1 in Formulas 1 and 2, we have:
[tex]\begin{gathered} AP^2=AD^2+DP^2\Rightarrow DP=\sqrt[]{AP^2-AD^2}=\sqrt[]{AP^2-x^2\cdot cm^2}\text{.} \\ \cos \theta=\frac{AD}{AP}=\frac{x\cdot cm}{AP}\text{.} \end{gathered}[/tex](2) Replacing the data of Triangle 2 in Formula 2, we have:
[tex]\cos \theta=\frac{ZP}{OP}=\frac{AP/2}{4cm}.[/tex](3) Equalling the right side of the equations with cos θ in (1) and (2), we get:
[tex]\frac{x\cdot cm}{AP}=\frac{AP/2}{4cm}.[/tex]Solving for AP², we get:
[tex]\begin{gathered} x\cdot cm=\frac{AP^2}{8cm}, \\ AP^2=8x\cdot cm^2\text{.} \end{gathered}[/tex](4) Replacing the expression of AP² in the equation for DP in (1), we have the equation for side DP in terms of x:
[tex]DP^{}=\sqrt[]{8x\cdot cm^2-x^2\cdot cm^2}=\sqrt[]{x\cdot(8-x)}\cdot cm\text{.}[/tex](ii) The area of a triangle is given by:
[tex]S=\frac{1}{2}\cdot base\cdot height.[/tex]In the case of triangle △ADP, we have:
• base = DP,
,• height = AD.
Replacing the values of DP and AD in the formula for S, we get:
[tex]S=\frac{1}{2}\cdot DP\cdot AD=\frac{1}{2}\cdot(\sqrt[]{x\cdot(8-x)}\cdot cm)\cdot(x\cdot cm)=\frac{x}{2}\cdot\sqrt[]{x\cdot(8-x)}\cdot cm^2.[/tex](b) Maximum value of S
We must find the maximum value of S in terms of x. To do that, we compute the first derivative of S(x):
[tex]\begin{gathered} S^{\prime}(x)=\frac{dS}{dx}=\frac{1}{2}\cdot\sqrt[]{x\cdot(8-x)}\cdot cm^2+\frac{x}{2}\cdot\frac{1}{2}\cdot\frac{8-2x}{\sqrt{x\cdot(8-x)}}\cdot cm^2 \\ =\frac{1}{2}\cdot\sqrt[]{x\cdot(8-x)}\cdot cm^2+\frac{x}{2}\cdot\frac{(4-x^{})}{\cdot\sqrt[]{x\cdot(8-x)}}\cdot cm^2 \\ =\frac{1}{2}\cdot\frac{x\cdot(8-x)+x\cdot(4-x)}{\sqrt[]{x\cdot(8-x)}}\cdot cm^2 \\ =\frac{x\cdot(6-x)}{\sqrt[]{x\cdot(8-x)}}\cdot cm^2\text{.} \end{gathered}[/tex]Now, we equal to zero the last equation and solve for x, we get:
[tex]S^{\prime}(x)=\frac{x\cdot(6-x)}{\sqrt[]{x\cdot(8-x)}}\cdot cm^2=0\Rightarrow x=6.[/tex]We have found that the value x = 6 maximizes the area S(x). Replacing x = 6 in S(x), we get the maximum area:
[tex]S(6)=\frac{6}{2}\cdot\sqrt[]{6\cdot(8-6)}\cdot cm^2=3\cdot\sqrt[]{12}\cdot cm^2=6\cdot\sqrt[]{3}\cdot cm^2.[/tex](c) Rate of change
We know that the length AD = x cm decreases at a rate of 1/√3 cm/s, so we have:
[tex]\frac{d(AD)}{dt}=\frac{d(x\cdot cm)}{dt}=\frac{dx}{dt}\cdot cm=-\frac{1}{\sqrt[]{3}}\cdot\frac{cm}{s}\Rightarrow\frac{dx}{dt}=-\frac{1}{\sqrt[]{3}}\cdot\frac{1}{s}\text{.}[/tex]The rate of change of the area S(x) is given by:
[tex]\frac{dS}{dt}=\frac{dS}{dx}\cdot\frac{dx}{dt}\text{.}[/tex]Where we have applied the chain rule for differentiation.
Replacing the expression obtained in (b) for dS/dx and the result obtained for dx/dt, we get:
[tex]\frac{dS}{dt}(x)=(\frac{x\cdot(6-x)}{\sqrt[]{x\cdot(8-x)}}\cdot cm^2\text{)}\cdot(-\frac{1}{\sqrt[]{3}}\cdot\frac{1}{s}\text{)}[/tex]Finally, we evaluate the last expression for x = 2, we get:
[tex]\frac{dS}{dt}(2)=(\frac{2\cdot(6-2)}{\sqrt[]{2\cdot(8-2)}}\cdot cm^2\text{)}\cdot(-\frac{1}{\sqrt[]{3}}\cdot\frac{1}{s})=-\frac{8}{\sqrt[]{12}}\cdot\frac{1}{\sqrt[]{3}}\cdot\frac{cm^2}{s}=-\frac{8}{\sqrt[]{36}}\cdot\frac{cm^2}{s}=-\frac{8}{6}\cdot\frac{cm^2}{s}=-\frac{4}{3}\cdot\frac{cm^2}{s}.[/tex]So the rate of change of the area of △ADP is -4/3 cm²/s.
Answers
(a)
• (i), Side DP in terms of x:
[tex]DP(x)=\sqrt[]{x\cdot(8-x)}\cdot cm\text{.}[/tex]• (ii), Area of ADP in terms of x:
[tex]S(x)=\frac{x}{2}\cdot\sqrt[]{x\cdot(8-x)}\cdot cm^2.[/tex](b) The maximum value of S is 6√3 cm².
(c) The rate of change of the area of △ADP is -4/3 cm²/s when x = 2.
I have the answers for the first two but now I'm just confused
O A. 1376 square inchesO B. 672 square inchesO C. 1562 square inchesO D. 936 square inches
The seat back cushion is a cuboid. The surafce area can be calculated below
[tex]\begin{gathered} l=26\text{ inches} \\ h=5\text{ inches} \\ w=18\text{ inches} \\ \text{surface area=2(}lw+wh+hl\text{)} \\ \text{surface area=}2(26\times18+18\times5+5\times26) \\ \text{surface area=}2(468+90+130) \\ \text{surface area=}2\times688 \\ \text{surface area}=1376inches^2 \end{gathered}[/tex]A net of arectangular pyramidis shown. Therectangular base haslength 24 cm andwidth 21 cm. Thenet of the pyramidhas length 69.2 cmand width 64.6 cm.Find the surfacearea of the pyramid.
Solution
The Image will be of help
To find x
[tex]\begin{gathered} x+24+x=69.2 \\ 2x+24=69.2 \\ 2x=69.2-24 \\ 2x=45.2 \\ x=\frac{45.2}{2} \\ x=22.6 \end{gathered}[/tex]To find y
[tex]\begin{gathered} y+21+y=64.6 \\ 2y+21=64.6 \\ 2y=64.6-21 \\ 2y=43.6 \\ y=\frac{43.6}{2} \\ y=21.8 \end{gathered}[/tex]The diagram below will help us to find the Surface Area of the Pyramid
The surface area is
[tex]SurfaceArea=A_1+2A_2+2A_3[/tex]To find A1
[tex]A_1=24\times21=504[/tex]To find A2
[tex]\begin{gathered} A_2=\frac{1}{2}b\times h \\ 2A_2=b\times h \\ 2A_2=21\times22.6 \\ 2A_2=474.6 \end{gathered}[/tex]To find A3
[tex]\begin{gathered} A_3=\frac{1}{2}bh \\ 2A_3=b\times h \\ 2A_3=24\times21.8 \\ 2A_3=523.2 \end{gathered}[/tex]The surface Area
[tex]\begin{gathered} SurfaceArea=A_1+2A_2+2A_3 \\ SurfaceArea=504+474.6+523.2 \\ SurfaceArea=1501.8cm^2 \end{gathered}[/tex]Thus,
[tex]SurfaceArea=1501.8cm^2[/tex]Do they have the same value? Is +3 equal to -3 and -10 equal to +10? Why?
+3 and -3 do not have the same value
+10 and -10 do not have the same value
Explanation:+3 is a positive number while -3 is a negative number
+3 ≠ -3 (Since one is positive and the other is negative)
The difference between +3 and -3 = 3 - (-3) = 6
Therefore, +3 and -3 do not have the same value
+10 is a positive number while -10 is a negative number
+10 ≠ -10 (Since one is positive and the other is negative)
The difference between +10 and -10 = 10 - (-10) = 20
Therefore, +10 and -10 do not have the same value
If triangle ABC with C =90°,if C = 31MM & B equals 57° then a equals
SOLUTION
Step1; Draw the Triangle and locate the angles
We are to obtain the value of a that is the side |BC|
Applying trigonometry ratios we have
[tex]\begin{gathered} \text{hypotenuse}=c=31 \\ \text{Adjacent}=a \\ \theta=57^0 \end{gathered}[/tex][tex]\begin{gathered} \cos \theta=\frac{adjacent}{Hypotenuse} \\ \cos 57^0=\frac{a}{31}\ldots.\text{ cross multiply} \\ a=31\times cos57^0 \end{gathered}[/tex][tex]\begin{gathered} a=31\times0.8999 \\ a=27.89 \end{gathered}[/tex]Then the value of a = 28mm to the nearest whole number
Evaluate the function: g(x)=-x+4Find: g(b-3)
The given function is:
[tex]g(x)=-x+4[/tex]Value of :
[tex]g(b-3)=?[/tex][tex]\begin{gathered} g(x)=-x+4 \\ x=b-3 \\ g(b-3)=-(b-3)+4 \\ g(b-3)=-b+3+4 \\ g(b-3)=7-b \end{gathered}[/tex]so the g(b-3) is 7-b.
Find the y-coordinate of point P that lies 1/3 along segment CD, closer to C, where C (6, -5) and D (-3, 4).
SOLUTION:
The given ratio is:
[tex]1:3[/tex]• The given points are ,C(6, -5) and D (-3, 4).
Using the section formula, the coordinate of P is:
[tex]\begin{gathered} P=(\frac{1(-3)+3(6)}{1+3},\frac{1(4)+3(-5)}{1+3}) \\ P=(\frac{-3+18}{4},\frac{4-15}{4}) \\ P=(\frac{15}{4},\frac{-11}{4}) \end{gathered}[/tex]Therefore the coordiantes of P
[tex]P=(\frac{15}{4},\frac{-11}{4})[/tex]which of the following terms best describes a group of equations in which at least one equation is nonlinear, all of the equations have the same variables, and all of the equations are used together to solve a problem?a) solution of nonlinear equationb) graph of nonlinear equationc) graph of linear equationsd) system of nonlinear equations
Solution
- The correct answer is "A system of nonlinear equations"
- This is because the definition of a system of nonlinear equations is is a system of two or more equations in two or more variables containing at least one equation that is not linear.
Final Answer
OPTION D
Find the component form of the sum of u and v with direction angles u and v.
We will have the following:
[tex]\begin{gathered} U_x=14cos(45) \\ \\ U_y=14sin(45) \\ \\ V_x=80cos(180) \\ \\ V_y=80sin(180) \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sum_x=\frac{14\sqrt{2}}{2}+(-80)\Rightarrow\sum=7\sqrt{2}-80 \\ \\ \sum_y=\frac{14\sqrt{2}}{2}+(0)\Rightarrow\sum=7\sqrt{2} \end{gathered}[/tex]So, the component form for the sum of the vectors will be:
[tex]u+v=(7\sqrt{2}-80)i+(7\sqrt{2})j[/tex]what is the answer to this? 3√5+15√5
what is the answer to this? 3√5+15√5
we have
3√5+15√5=18√5
answer is 18√5Which of the following is not a valid way of starting the process of factoring60x² +84x +49?Choose the inappropriate beginning below.O A. (x )(60)OB. (2x (30%)O C. (6x X10x)OD. (2x (5x )
Given the equation:
60x^2 + 84x + 49
We are to determine among the options which is not a process of factorizing.
In factorizing, you get factors of the given numbers of the equation that when they are being multiplied or added, they give the numbers in the equation.
So, looking at the options, the only option that does not satisfies the requirement for starting a factorization process is B, which is (2x (30%)
Therefore, the inappropriate process of starting factorization among the option is option B which is (2x (30%).
Solve the following inequality for t. Write your answer in the simplest form.6t + 3 < 7t + 10
Therefore, the solution is t > -7.
First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle 0.
The trigonometric functions are given by the following formulas:
[tex]\begin{gathered} \sin \theta=\frac{a}{h} \\ \cos \theta=\frac{b}{h} \\ \tan \theta=\frac{a}{b} \\ \cot \theta=\frac{b}{a} \\ \sec \theta=\frac{h}{b} \\ \csc \theta=\frac{h}{a} \end{gathered}[/tex]Where we call a to the opposite leg to the angle θ (the side whose measure equals 20), b is the adjacent leg to angle θ (the side whose measure equals 21) and we call h to the hypotenuse (the larger side, whose measure equals 29).
By replacing 20 for a, 21 for b and 29 for h into the above formulas, we get:
[tex]\begin{gathered} \sin \theta=\frac{20}{29} \\ \cos \theta=\frac{21}{29} \\ \tan \theta=\frac{20}{21} \\ \csc \theta=\frac{29}{20} \\ \sec \theta=\frac{29}{21} \\ \cot \theta=\frac{21}{20} \end{gathered}[/tex]An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
To solve more questions on unitary method, visit the link below-
https://brainly.com/question/13659834
#SPJ1